I have defined a first order system and a PI controller as follows: and
In matlab code
Gc = tf([1 alpha],[1 0]);
The controller should also have a gain value and I'm varying it from 0 to 10. My expectation is that, because of the PI-controller, the step response goes to 1 eventually for all gain values I choose. It does so, for gain values up to 8, but for a gain value of 9, I observe something strange. Could you help me explaining this phenomenon?
My code to draw the step responses for the PI-controlled system is
T = feedback(9*G_openloop,1)
Even if I compute the DC gain, it goes to 1, but the stepplot doesn't.
For the green line (K = 9) a strange bending of the curve occurs around time 2 seconds and the green line never goes to its steady state of 1.